Fakery: High Resolution Fluid Sim
You definitely don't want to use a fluid simulation for rain. I'd use a particles system for the general rain in the scene. You can use Dynamic paint to make the particles interact with a "water" surface to make ripples (without actually using fluid sim).

For the arrow piercing a raindrop, that's more like a hero shot, up close in the foreground. I'd probably use soft body physics on the raindrop as it will be large in the shot (possibly), and at that size the surface tension of the water drop will be more like a gel object instead of flowing water (until it bursts). The trick is once the arrow pierces through and breaks the surface tension. At that point you do want something more like a fluid sim effect to show the displaced water splashing out around the arrow.

Here's a quick mockup of the fluid sim for the hero rain drop. Note I went for a slow motion look and decreased the gravity to -1m/s2.